The move came as the Prime Minister offered his own concession, apologising for breakdowns in the two countries' relationship under Labor over boatpeople and live cattle exports as well as admitting the rhetoric from all sides of Australian politics on people-smuggling might have gone too far.

However the most controversial issue between Australia and Indonesia, the Coalition's policy of turning back boats when safe to do so, was not discussed at last night's summit.This was confirmed to The Australian last night by Security Co-ordinating Minister Djoko Suyanto, who will be in charge of asylum-seeker policy co-ordination with Australia.

After the leaders' meeting, Dr Yudhoyono and Mr Abbott flagged further direct bilateral talks on people-smuggling between General Djoko and Immigration Minister Scott Morrison.

"We realise, apart from the Bali process, we need another kind of co-operation at the bilateral level between Indonesia and Australia," Dr Yudhoyono said.

The President said both Australia and Indonesia had become "victims" of people smugglers.

Mark Binskin, acting commander of the Abbott government's Operation Sovereign Borders, said yesterday three boatloads of suspected asylum-seekers had been intercepted by Australian authorities in the past week and 128 people had been sent for offshore processing to Manus Island and Nauru.

However, these figures did not include about 81 men, women and children who were offloaded at Christmas Island yesterday, outside the reporting period.Indonesia's insistence on working through the Bali Process and unhappiness with the Coalition's "unilateralist" approach was at the centre of the row that came to a head last week.

Indonesian Foreign Minister Marty Natalegawa warned Julie Bishop that the Coalition's approach "potentially risk(ed) the close co-operation and trust between the two countries that has been established through Bali Process".

Dr Yudhoyono's encouragement for bilateral action, as well as working with the Bali Process framework, was a clear signal the President wanted the dispute curtailed immediately."It would be much better if cooperation at the bilateral level would flow even further, based on the Bali Process, so we may both together overcome the challenge of people smugglers.

"Dr Natalegawa last night seemed to step backwards, in describing the turn-back issue as a "technical aspect" of bilateral cooperation on people-smuggling.

"Well, the technical aspects of ways and means to deal with this issue will be discussed at technical level, but the main spirit during the leaders' meeting is . . . absolute respect for the sovereignty of Indonesia that (has) been constantly repeated by Prime Minister Abbott. This is the point that Prime Minister Abbott has constantly emphasised. The key terminology that has been discussed is towards the idea of co-ordination.

"Mr Abbott said he had had a "very frank" discussion about issues of sovereignty and issues of people smuggling with Dr Yudhoyono. He said people-smuggling was an issue of sovereignty for Australia and he appreciated how seriously Indonesia had taken the issue in the past.

"And I look forward to working even more co-operatively with Indonesia in the future," he said. "But I want to state publicly as well as privately, Mr President, Australia's total respect for Indonesia's sovereignty, total respect for Indonesia's territorial integrity.

"He said much of the detail on talks between Indonesia and Australia would be left to talks between the ministers involved, General Djoko and Mr Morrison."We are determined to end this scourge which is not just an affront to our two countries but which has become a humanitarian disaster in the sea between our two countries," he said.

Mr Abbott also moved to reassure Indonesia over West Papua, saying "the government of Australia takes a very dim view, a very dim view indeed of anyone seeking to use our country as a platform for grandstanding against Indonesia".

Later last night, Mr Abbott invoked the co-operation between the two nations during the hunt for the Bali bombers, telling an official dinner at the Presidential Palace "our relationship has so much promise and everything will be easier once the people-smuggling complication is gone".

Mr Abbott used his first overseas speech since taking office to admit there had been Australian mistakes in the relationship.

"There have been times, I'm sorry to say, when Australia must have tried your patience: when we 'put the sugar on the table' for people-smugglers; or cancelled the live cattle trade in panic at a TV program. There have been times when all sides of Australian politics should have said less and done more. I am confident that these will soon seem like out-of-character aberrations and that the relationship will once more be one of no surprises, based on mutual trust, dependability and absolute respect for each other's sovereignty under the Lombok Treaty.

"His concession comes after weeks of building tensions with Indonesia over asylum-seekers, fanned in recent days by the death of more than 50 asylum-seekers when a boat sank just off the coast of Java last week.

As Mr Abbott moved to defuse the sensitivities, senior business leaders cautioned the asylum-seeker issue and old stereotypes still dominant in the Australian community about Indonesia and its people threatened to derail fresh talks on trade and investment, which could see Australia fall out of the top 10 trading partners with its closest neighbour.

ANZ chief executive Mike Smith said the Indonesia relationship was "very important" to Australia. "Quite clearly the boatpeople issue needs to be addressed," he said. "The most important thing is to ensure it does not derail the important trade, economic and investment issues which should be at the front of the agenda.

"Mr Abbott last night described Indonesia as a "true friend" whose actions would "never be forgotten - just as Australia will never forget Indonesia's work to bring to justice the killers of so many innocent people, including nearly 100 Australians, after the Bali and Jakarta bombings".

Australia, he said, stood by Indonesia during the Asian financial crisis and at the time of the devastating East Asian tsunami, and Australia and Indonesia had also worked together in counter terrorism after the Bali bombings.

Steve Nicholson, chief executive of the Australian affiliate of Indonesia's largest company, Asia Pulp and Paper, said the relationship could not be mended while there was an undercurrent of distrust among the Australian public and business community.

"All aspects of our community, the business community included, need to banish their old school and inaccurate views about Indonesia to gain a greater understanding of the modern country," he writes in The Australian today.

He pointed to a recent study by the Department of Foreign Affairs and Trade showing that almost 50 per cent of Australians still believed Indonesia was a threat to Australia's security.

Last night, in a step to boost relations between the two countries, Mr Abbott announced the establishment of the Australian Centre for Indonesian Studies. Its mandate would be to "strengthen and deepen Australia-Indonesia business, cultural, educational, research and community links".

The centre will be headquartered at Monash University, with nodes at the Australian National University and the University of Melbourne. The CSIRO will also be a partner, as will the Victorian government.